login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A268886 T(n,k)=Number of nXk binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once. 13

%I #4 Feb 15 2016 11:33:56

%S 0,1,0,2,5,0,5,14,20,0,10,54,84,71,0,20,158,501,462,235,0,38,475,2190,

%T 4133,2418,744,0,71,1340,9996,27130,31956,12252,2285,0,130,3740,42362,

%U 186732,317966,236960,60666,6865,0,235,10204,178400,1187838,3283890

%N T(n,k)=Number of nXk binary arrays with some element plus some horizontally or antidiagonally adjacent neighbor totalling two exactly once.

%C Table starts

%C .0.....1.......2.........5..........10............20..............38

%C .0.....5......14........54.........158...........475............1340

%C .0....20......84.......501........2190..........9996...........42362

%C .0....71.....462......4133.......27130........186732.........1187838

%C .0...235....2418.....31956......317966.......3283890........31427480

%C .0...744...12252....236960.....3596174......55491832.......800733668

%C .0..2285...60666...1706732....39670270.....911930096.....19876401224

%C .0..6865..295230..12034000...429588382...14681855846....483987898760

%C .0.20284.1417452..83485488..4585939726..232688402028..11611969197776

%C .0.59155.6732102.571836176.48401059362.3642322709900.275345016177616

%H R. H. Hardin, <a href="/A268886/b268886.txt">Table of n, a(n) for n = 1..799</a>

%F Empirical for column k:

%F k=1: a(n) = a(n-1)

%F k=2: a(n) = 6*a(n-1) -11*a(n-2) +6*a(n-3) -a(n-4)

%F k=3: a(n) = 10*a(n-1) -31*a(n-2) +30*a(n-3) -9*a(n-4)

%F k=4: a(n) = 16*a(n-1) -88*a(n-2) +200*a(n-3) -208*a(n-4) +96*a(n-5) -16*a(n-6) for n>7

%F k=5: [order 8] for n>9

%F k=6: [order 10] for n>12

%F k=7: [order 14] for n>16

%F Empirical for row n:

%F n=1: a(n) = 2*a(n-1) +a(n-2) -2*a(n-3) -a(n-4)

%F n=2: a(n) = 2*a(n-1) +5*a(n-2) -4*a(n-3) -11*a(n-4) -6*a(n-5) -a(n-6)

%F n=3: [order 9]

%F n=4: [order 16]

%F n=5: [order 26]

%F n=6: [order 42]

%F n=7: [order 68]

%e Some solutions for n=4 k=4

%e ..0..1..0..0. .0..0..0..0. .0..0..1..0. .0..0..0..0. .0..1..0..0

%e ..0..0..0..1. .0..1..0..1. .1..0..0..1. .0..0..1..1. .0..1..0..0

%e ..0..0..1..0. .1..0..0..0. .1..0..0..0. .0..0..0..0. .0..1..0..0

%e ..1..0..1..0. .1..0..0..1. .1..1..0..1. .0..1..0..0. .1..0..0..0

%Y Column 2 is A054444(n-1).

%Y Row 1 is A001629.

%K nonn,tabl

%O 1,4

%A _R. H. Hardin_, Feb 15 2016

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)